TL;DR: In this article, a solution for the radius of the vapor bubble as a function of time is obtained which is valid for sufficiently large radius, since the radius at which it becomes valid is near the lower limit of experimental observation.
Abstract: The growth of a vapor bubble in a superheated liquid is controlled by three factors: the inertia of the liquid, the surface tension, and the vapor pressure. As the bubble grows, evaporation takes place at the bubble boundary, and the temperature and vapor pressure in the bubble are thereby decreased. The heat inflow requirement of evaporation, however, depends on the rate of bubble growth, so that the dynamic problem is linked with a heat diffusion problem. Since the heat diffusion problem has been solved, a quantitative formulation of the dynamic problem can be given. A solution for the radius of the vapor bubble as a function of time is obtained which is valid for sufficiently large radius. This asymptotic solution covers the range of physical interest since the radius at which it becomes valid is near the lower limit of experimental observation. It shows the strong effect of heat diffusion on the rate of bubble growth. Comparison of the predicted radius‐time behavior is made with experimental observations in superheated water, and very good agreement is found.
TL;DR: In this paper, the phase behavior of reservoir fluids is analyzed and a model for phase behavior in real reservoir fluid simulations is presented. But the model is not suitable for the simulation of real reservoir fluids.
Abstract: Preface. Nomenclature. Phase Behaviour Fundamentals. Reservoir Fluid Composition. Phase Behaviour. Pure compound. Corresponding states. Multicomponent mixture. Classification of Reservoir Fluids. Dry gas. Wet gas. Gas condensate. Volatile oil. Black oil. References. Exercises. PVT Tests and Correlations. Fluid Sampling. Well preparation. Sample collection. PVT Tests 38. Dry gas. Wet gas. Black oil. Gas condensate. Volatile oil. Emperical Correlations. Black oil. (Bubble point pressure. Gas in solution. Oil formation volume factor. Total formation volume factor. Oil density. Oil viscosity). Natural gas. (Volumetric data. Gas viscosity). Formation water. (Water content of hydrocarbon phase. Hydrocarbon solubility in water. Water formation volume factor. Compressibility of water. Water density. Water viscosity). References. Exercises. Phase Equilibria. Criteria for Equilibrium. Chemical potential. Fugacity. Activity. Equilibrium Ratio. Raoult's law. Henry's law. Emperical correlations. References. Exercises. Equations of State. Viral EOS and its Modifications. Starling-Benedict-Webb-Rubin EOS. Cubic Equations of State. Two-parameter EOS. (Soave-Redlich-Kwong EOS. Peng-Robinson EOS. Volume shift). Three-parameter EOS. (Schmidt-Wenzel EOS, Patel-Teja EOS). Attracting term temperature dependency. Mixing Rules. Random mixing rules. Non-random mixing rules. References. Exercises. Phase Behaviour Calculations. Vapour-Liquid Equilibrium Calculations. Root selection. Rapid flash calculations. Stability Analysis. Stability limit. Critical Point Calculations. Compositional Grading. Equilibrium assumption. Non-equilibrium fluids. Heat of transport. Significance. References. Exercises. Fluid Characterisation. Experimental Methods. Distillation. Gas chromatography. Critical properties. Lee-Kesler correlations. Riazi-Daubert correlations. Perturbation expansion correlations. Description of Fluid Heavy End. Single carbon number function. Continuous description. Direct application. References. Exercises. Gas Injection. Miscibility Concepts. Miscibility in Real Reservoir Fluids. Experimental Studies. Slim tube. Rising bubble apparatus. Contact experiments. Prediction of Miscibility Conditions. First contact miscibility. Vaporising gas drive. Condensing-vaporising gas drive. References. Exercises. Interfacial Tension. Measurement Methods. Prediction of Interfacial Tension. Parachor method. Corresponding states correlation. Comparison of predictive methods. Water-Hydrocarbon Interfacial Tension. References. Exercises. Application in Reservoir Simulation. Grouping. Group selection. Group properties. Composition retrieval. Comparison of EOS. Phase composition. Saturation pressure. Density. Gas and liquid volumes. Robustness. Tuning of EOS. Fluid characterisation. Selection of EOS. Experimental data. Selection of regression variables. Limits of tuned parameters. Methodology. Dynamic Validation of Model. Relative permeability function. Viscosity prediction.
TL;DR: In this paper, the authors derived analytical expressions for bubble radii and growth rates in an analysis of surface boiling at high heat transfer rates and showed that the product of bubble radius and radial velocity is a constant.
Abstract: Analytical expressions for bubble radii and growth rates derived by the authors are applied in an analysis of surface boiling at high heat transfer rates. It is shown that the product of bubble radius and radial velocity is a constant, independent of the bubble radius. This circumstance permits the formulation of a Reynolds number for the flow in the thin superheated liquid layer adjacent to the heating surface. The result of the analysis is then applied to maximal heat transfer rates in pool boiling.
TL;DR: In this article, a criterion for bubble initiation from a gas filled cavity on a surface in contact with a superheated layer of liquid was developed, and it was found that the temperature of bubble initiation on a given surface is a function of the temperature conditions in the liquid surrounding the cavity as well as the surface properties themselves.
TL;DR: In this article, a photographic study was made to investigate the boiling phenomena in the neighborhood of the critical heat flux, and a dimensionless relationship was developed relating bubble velocity, bubble diameter, and contact angle at breakoff.
Abstract: A photographic study was made to investigate the boiling phenomena in the neighborhood of the critical heat flux. The system consisted of an electrically heated zirconium ribbon, insulated on its underface, suspended in a pool of water at its saturation temperature. Measurements of bubble diameters, bubble positions relative to the heating surface, local bubble frequencies, and contact angles at known times intervals were obtained from the film. Results indicate that at high heat fluxes the primary forces acting on a bubble leaving the surface are the buoyancy and drag forces. A dimensionless relationship is developed relating bubble velocity, bubble diameter, and contact angle at breakoff. Drag coefficients for freely rising vapor bubbles a saturated liquid are found to be representable by the usual drag coefficient-Reynolds number curves for solid bodies. Jakob's plot of bubble frequency vs. bubble diameter at breakoff is extended to high heat-flux values, and a relationship proposed by Deissler at the critical heat flux is found to yield reasonable agreement with the experimental data.